Edge-Mode Lasing in 1D Topological Active Arrays

We report the first observation of lasing topological edge states in a 1D Su-Schrieffer-Heeger active array of microring resonators. We show that the judicious use of non-Hermiticity can promote single edge-mode lasing in such arrays. Our experimental and theoretical results demonstrate that, in the presence of chiral-time symmetry, this non-Hermitian topological structure can experience phase transitions that are dictated by a complex geometric phase. Our work may pave the way towards understanding the fundamental aspects associated with the interplay among non-Hermiticity, nonlinearity, and topology in active systems.

Figure 1

(a) InGaAsP multilayer quantum well structure used in the microrings, (b) a schematic of the SSH microring laser array, and (c) a microscope image of the fabricated structure with 16 elements. The insets show scanning electron microscope images of the grating at the end of the outcoupling waveguides and the coupling region between two microrings.

Figure 2

Eigenvalue diagrams of an infinite (a) Hermitian and uniformly pumped ($g=0$ and $g\ne 0$) and (b) $\mathcal{P}\mathcal{T}$-symmetric SSH lattice, where the eigenvalues of the edge modes corresponding to a finite, nontrivial termination of the structure are also represented by dots at both ends of the Brillouin zone. The field profiles of the edge states are also depicted in the right and left insets.

Figure 3

Theoretically predicted steady-state lasing profiles for (a) uniformly pumped and (b) $\mathcal{P}\mathcal{T}$-symmetric SSH lattice. Panels (c) and (d) depict the power spectra corresponding to the edge mode and bulk modes as obtained from different locations in the array.

Figure 4

Complex band structure of the infinite $\mathcal{P}\mathcal{T}$-symmetric SSH model, where (a), (b), and (c) correspond to the three phases I, II, and III, respectively (the eigenvalues of the edge modes corresponding to a finite, nontrivial termination of the structure are depicted by dots at both ends of the Brillouin zone). The insets show the simulated intensity distributions corresponding to these three distinct regimes, as obtained from Eqs. (3). Panel (d) presents the complex Berry phase ${\mathrm{\Phi }}_{-}$ as a function of the normalized gain coefficient $\eta$.

Figure 5

The left panels depict the measured intensity distributions in the 16-element SSH array at every site. The middle panels show raw data from the extraction ports, while the right panels the corresponding power spectra. Each of the successive rows (a), (b), and (c) are progressively associated with phase I, II, and III observations. The inset in (a) provides the exponential intensity distribution of the lasing edge state in a log-linear scale.